LDA is slow, so is it worth researching?

The replicated softmax is an undirected topic model that dramatically outperforms LDA in terms of log prob and allows fast deterministic inference using a single forward pass. Since the probabilistic model is a lot better and the inference is easy, you should consider it. Depending on the requirement of your application, it may or may not be appropriate. For instance, it does not yield easily-interpretable topics by itself (you would have to put LDA or something on top of it for that), but if you care more about having a good model and less about reading topic tea leaves, it might be useful.

More generally, researching any topic even if it isn't a computationally feasible method, isn't necessarily a bad idea. 20-25 years ago, people were researching algorithms like the Boltzmann Machine -- an algorithm that, while powerful, wasn't computationally feasible on hardware generally available at the time particularly with the training algorithms that were known.

Yet, some people studied/researched them and were able to build on the idea. At some point it became a viable algorithm.

The speed of LDA depends on the implementation. I think the implementation in vowpal-wabbit, for example, should be faster than most implementations of PLSA.

LDA is more interestin g as a building block than as a thing in itself. In this it is not so different from PLSA (it is PLSA with priors), but more useful in a larger context. See for example this list of interesting papers that are based on and use LDA.